No, there is not much difference between normal colleges and ordinary undergraduate courses. It's just that the diploma says that I graduated from a normal university/college, and my degree certificate is the same as that of an ordinary university. Only some majors can only be teachers. You said that a student majoring in mathematics and applied mathematics wants to work related to his major, can he do other jobs? I can only be a teacher and teach mathematics. Other majors, such as education and political science, are most likely to be teachers, but if they are other majors, they are just like ordinary undergraduates, such as accounting.
In short, it has a lot to do with the major. If the major has nothing to do with the teaching profession, you can not be a teacher. If the relationship is close and you don't want to change careers, you can only be a teacher, except for postgraduate entrance examination, self-taught examination and second degree.